Please Help Today- Statistics Question

Question

A particular fruit's weights are normally distributed, with a mean of 721 grams and a standard deviation of 32 grams.

If you pick 23 fruit at random, what is the probability that their mean weight will be between 718 grams and 743 grams (Give answer to 4 decimal places.)

If I can solve this one, I'll be able to solve several like it.

Answer 1

xbar = mean fruit weight

Want to compute P(718 < xbar < 743)

z-statistic = (xbar - population mean)/(population standard deviation/square root(sample size))

= (xbar - 721)/(32/sqrt(23)) = (xbar - 721)/6.67

Compute z-statistic for xbar = 718 and 743:

P((718-721)/6.67 < z < (743-721)/6.67) = P(-0.45 < z < 3.3) = P(z < 3.3) - P(z < -0.45) = 0.9995 - 0.3264 = 0.6731.